A bearingless compound rotor cage asynchronous motor multi-frequency harmonic vibration compensation control method and system

Abstract

The application relates to the technical field of electric transmission and control, and discloses a bearing-free composite rotor cage asynchronous motor multi-frequency harmonic vibration compensation control method and system. The bearing-free composite rotor cage asynchronous motor multi-frequency harmonic vibration compensation control method comprises the following steps: collecting a bearing-free composite rotor cage asynchronous motor rotor radial displacement signal; constructing an input vector containing a direct current item and multi-order cosine and sine components; using an adaptive linear neuron algorithm to decompose the signal and extract direct current, a fundamental wave and each order harmonic component; using an extended linear active disturbance rejection controller to observe total disturbance containing low-frequency slow change and harmonic disturbance; calculating compensation force according to the harmonic component; superimposing the compensation force and basic suspension force to form a total control force instruction; driving a suspension winding through force-current conversion; and inhibiting multi-frequency harmonic vibration. The application effectively improves harmonic separation precision and disturbance suppression capacity, and provides a reliable theoretical guarantee for high-speed bearing-free motor control.

Description

Technical Field

[0001] This invention relates to the field of electrical drive and control technology, and more specifically, to a method and system for multi-frequency harmonic vibration compensation control of a bearingless composite rotor cage asynchronous motor. Background Technology

[0002] Asynchronous motors are widely used in industrial drives and energy equipment due to their simple structure, low cost and reliable operation.

[0003] However, its operation relies on mechanical bearings, and long-term operation can easily lead to friction, wear, and lubrication failure, thus limiting the application of the motor in high-speed, contactless, and long-life applications. Therefore, a bearingless composite rotor squirrel-cage asynchronous motor with suspendable bearings has been proposed. However, bearingless motors are highly susceptible to the effects of rotor eccentricity and uneven mass under high-speed conditions, which can induce periodic excitation forces with amplitude increasing with the square of the speed, leading to bearing vibration.

[0004] For existing research on harmonic vibration suppression in bearingless composite rotor squirrel-cage induction motors, current studies have gradually transitioned from single fundamental frequency compensation to multi-frequency harmonic suppression, demonstrating the necessity and feasibility of multi-frequency signal control. However, current solutions mainly focus on the RC / MRC route, which generally suffers from problems such as complex implementation, limited convergence speed, and insufficient adaptability to changes in operating conditions. Summary of the Invention

[0005] This invention provides a method and system for compensating and controlling multi-frequency harmonic vibration of a bearingless composite rotor squirrel-cage asynchronous motor, which solves the technical problem in related technologies that easily induces multi-frequency harmonic vibration and threatens suspension stability.

[0006] This invention provides a method for compensating and controlling multi-frequency harmonic vibration of a bearingless composite rotor squirrel-cage asynchronous motor, comprising the following steps:

[0007] Real-time acquisition of rotor radial displacement signals of bearingless composite rotor squirrel-cage asynchronous motor;

[0008] An input vector containing a DC term and multiple cosine and sine components is constructed. The displacement signal is decomposed in real time using an adaptive linear neuron algorithm to extract the DC component, fundamental component, and harmonic components.

[0009] An extended linear active disturbance rejection controller is used to observe the total disturbance of the system, which includes low-frequency slow-varying disturbances and harmonic disturbances;

[0010] Calculate the corresponding harmonic compensation force based on the extracted harmonic components;

[0011] The harmonic compensation force is superimposed with the basic levitation force output by the extended linear active disturbance rejection controller to generate a total control force command;

[0012] The total control force command is converted into force and current to drive the suspension winding, thereby suppressing the multi-frequency harmonic vibration of the rotor.

[0013] Furthermore, the real-time decomposition of the displacement signal using the adaptive linear neuron algorithm specifically includes:

[0014] Construct an input vector that includes a DC term 1 and cosine and sine components from the fundamental frequency to the Nth order;

[0015] Initialize the weight matrices for the x and y axes;

[0016] The displacement is estimated by a linear combination of the weight matrix and the input vector;

[0017] Calculate the error between the actual displacement and the estimated displacement;

[0018] The normalized least mean square algorithm is used to update the weight matrix. Its update law is: the increment of the weight is equal to the ratio of the adaptive step size to the input vector energy normalization factor multiplied by the product of the error and the input vector.

[0019] The amplitude and phase information of each harmonic are extracted from the updated weight matrix.

[0020] Furthermore, the adaptive step size is dynamically adjusted according to the estimation error, specifically as follows:

[0021] The adaptive step size is equal to the ratio of the maximum step size to the absolute value of the error multiplied by the reciprocal of the sum of the absolute value of the error and the smoothing factor;

[0022] The maximum step size is between 0 and 2 to ensure the convergence of the algorithm.

[0023] Furthermore, the extended linear active disturbance rejection controller includes:

[0024] A linear extended state observer is used to estimate three state variables: displacement, velocity, and total disturbance.

[0025] A bandwidth scheduling mechanism dynamically adjusts the observer bandwidth based on rotational speed and highest harmonic order.

[0026] The magnetic saturation adaptive gain module adjusts the control gain based on the observed magnetic flux linkage values.

[0027] A linear state error feedback control law generates a control output based on displacement error and velocity estimation.

[0028] Furthermore, the bandwidth scheduling mechanism is specifically as follows:

[0029] The observer bandwidth is taken as the larger value between the base bandwidth and the speed-related bandwidth, and is limited to between the preset minimum and maximum values;

[0030] The speed-related bandwidth is equal to the product of the bandwidth coefficient and the highest harmonic order and the rotor angular velocity;

[0031] The observer bandwidth is always maintained at 3 to 5 times the controller bandwidth to ensure time scale separation.

[0032] Furthermore, the gain adjustment strategy of the magnetic saturation adaptive gain module is as follows:

[0033] The adaptive gain is equal to the product of the base gain and the hyperbolic tangent function;

[0034] The independent variable of the hyperbolic tangent function is the ratio of the flux linkage saturation threshold to the sum of the observed flux linkage amplitude and the smoothing term;

[0035] When the observed magnetic link approaches the saturation threshold, the adaptive gain automatically decreases.

[0036] Furthermore, the calculation of harmonic compensation force specifically includes:

[0037] Multiply each extracted harmonic component by its corresponding compensation gain coefficient;

[0038] Sum all harmonic compensation force components;

[0039] The compensation force is smoothly limited by a nonlinear limiting function to prevent overcompensation.

[0040] Furthermore, the nonlinear limiting function is:

[0041] The compensation force after limiting is equal to the product of the time-varying gain coefficient, the maximum compensation force limit, and the hyperbolic tangent function;

[0042] The independent variable of the hyperbolic tangent function is the ratio of the compensating force to the maximum compensating force limit.

[0043] Furthermore, it also includes:

[0044] The highest harmonic order N that needs to be compensated is determined based on power spectral density analysis.

[0045] When the rotational speed change exceeds a preset threshold, the frequency component in the input vector is dynamically updated.

[0046] The control method is executed in a digital signal processor at a fixed sampling frequency.

[0047] This invention provides a multi-frequency harmonic vibration compensation control system for a bearingless composite rotor squirrel-cage asynchronous motor, used to execute the aforementioned multi-frequency harmonic vibration compensation control method for a bearingless composite rotor squirrel-cage asynchronous motor, comprising:

[0048] The displacement sensor module is used to acquire the radial displacement of the rotor in the x and y axes in real time.

[0049] The adaptive harmonic decomposition module is used to implement the adaptive linear neuron algorithm to decompose the displacement signal and extract the harmonic components of each order.

[0050] An extended active disturbance rejection control module is used to observe the total disturbance of the system and generate basic levitation force commands;

[0051] The harmonic compensation force calculation module is used to generate compensation force based on harmonic components;

[0052] Force synthesis module, used to superimpose basic levitation force and harmonic compensation force;

[0053] Force-to-current conversion module, used to convert force commands into current commands;

[0054] The power drive module is used to drive the suspension winding to generate electromagnetic levitation force.

[0055] The beneficial effects of this invention are: it effectively improves the accuracy of harmonic separation and the ability to suppress disturbances, and provides a reliable theoretical guarantee for the control of high-speed bearingless motors. Attached Figure Description

[0056] Figure 1 This is a flowchart of the bearingless composite rotor cage asynchronous motor multi-frequency harmonic vibration compensation control method of the present invention;

[0057] Figure 2 This is a stable interval diagram of the step size μ of the NLMS algorithm of this invention;

[0058] Figure 3 This is a convergence curve of the x and y axis weight error norms at a rotational speed of 3000 r / min (50 Hz) according to the present invention;

[0059] Figure 4 This is a convergence curve of the x and y axis weight error norms at a rotational speed of 6000 r / min (100 Hz) according to the present invention;

[0060] Figure 5 These are convergence plots of the amplitude estimation for each harmonic of this invention;

[0061] Figure 6 This is a convergence characteristic diagram of the weight error norm under different µmax settings of the present invention;

[0062] Figure 7 This is a structural diagram of the multi-harmonic NLMS displacement estimator for the x-axis channel of the present invention;

[0063] Figure 8This is a structural diagram of the multi-harmonic NLMS displacement estimator for the y-axis channel of the present invention;

[0064] Figure 9 This is a block diagram of the LADRC levitation force control of the present invention;

[0065] Figure 10 It is a sensitivity diagram of the root mean square (RMS) of rotor displacement to bandwidth ratio and harmonic gain.

[0066] Figure 11 This is a block diagram of the improved ELADRC suspension force control.

[0067] Figure 12 This is an energy coverage diagram of displacement signals under different harmonic orders;

[0068] Figure 13 This is the overall framework diagram of the multi-frequency harmonic vibration compensation control system;

[0069] Figure 14 These are the rotor speed simulation response diagrams under four control strategies;

[0070] Figure 15 This is a simulation comparison of the x-axis vibration amplitude under four control strategies;

[0071] Figure 16 These are simulation comparison graphs of the y-axis vibration amplitude under four control strategies;

[0072] Figure 17 This is a rotor trajectory diagram under the traditional PID suspension force control strategy;

[0073] Figure 18 This is the rotor trajectory diagram under the LADRC control strategy without harmonic compensation;

[0074] Figure 19 This is a rotor trajectory diagram under the Adaline / NLMS–ELADRC control strategy with only fundamental frequency compensation;

[0075] Figure 20 This is a rotor trajectory diagram under the multi-frequency compensation Adaline–ELADRC control strategy;

[0076] Figure 21 This is a diagram of the CCR-BIM experimental platform;

[0077] Figure 22 These are experimental response graphs of rotor speed under four control strategies;

[0078] Figure 23 This is a comparison chart of x-axis vibration amplitude under four control strategies;

[0079] Figure 24This is a comparison chart of the y-axis vibration amplitude under four control strategies;

[0080] Figure 25 These are rotor trajectory diagrams under four control strategies. Detailed Implementation

[0081] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0082] Example 1

[0083] This embodiment provides a method for multi-frequency harmonic vibration compensation control of a bearingless composite rotor squirrel-cage asynchronous motor, such as... Figure 1 As shown, the method includes the following steps:

[0084] Step 1: Double-layer multi-harmonic vibration compensation;

[0085] The Adaline / NLMS harmonic decomposition layer separates the DC, fundamental, and harmonic components by performing real-time multi-frequency expansion on the displacement signal.

[0086] Step 101, Signal Input and Model Definition:

[0087] The eddy current sensor acquires displacement signals x(k) and y(k) in real time along the x and y axes. The input vector R(k) is constructed as follows:

[0088]

[0089] Where T is the sampling period and n is the harmonic order.

[0090] The corresponding weight matrices for the x and y axes are:

[0091]

[0092] The weight matrix is ​​used to characterize the harmonic coefficients of the two channels respectively.

[0093] Step 102, Displacement estimation and error calculation:

[0094] By using a linear combination of the weight matrix and the input vector, the estimated displacements along the x-axis and y-axis can be obtained as follows:

[0095]

[0096]

[0097] The difference between the actual displacement and the actual displacement is defined as the estimation error:

[0098]

[0099] Where x(k) and y(k) represent the actual rotor displacement collected by the displacement sensor at time k, and εx(k) and εy(k) represent the model estimation bias at time k.

[0100] Step 103, Weight Update and Stability Analysis:

[0101] After obtaining the estimation errors εx(k) and εy(k), the weight matrix needs to be adjusted in real time using an adaptive algorithm to ensure the convergence and steady-state accuracy of harmonic decomposition under varying speed and disturbance conditions. While the traditional LMS update law is simple, it is difficult to balance convergence speed and steady-state accuracy under high-speed operation and multi-frequency signals. Therefore, this paper introduces the Normalized Least Mean Square (NLMS) algorithm, which normalizes the step size using the input vector energy, thereby improving the stability and convergence speed of the update.

[0102] Therefore, the update law of the weight matrix can be written as:

[0103]

[0104] μ x (k) and μ y (k) is the adaptive step size:

[0105]

[0106] To prove the convergence of the algorithm, a weight error vector is defined. And construct the Lyapunov function:

[0107]

[0108] Substituting into the update law, we get:

[0109]

[0110] Therefore, when , There is always The system is asymptotically stable. Combining the formula, as long as we choose... , The above conditions will always hold true.

[0111] Figure 2Stability analysis results of the NLMS algorithm under the Lyapunov framework are presented. It can be observed that when the step size satisfies 0 < μ < 2, the weight iteration converges, thus ensuring the reliability of harmonic decomposition and compensation force generation.

[0112] To further verify the correctness of the above stability analysis, this paper tests the convergence characteristics of the NLMS weights under two operating conditions: 3000 r / min and 6000 r / min. Figure 3 and Figure 4 As shown, under both 3000 r / min (50 Hz) and 6000 r / min (100 Hz) operating conditions, the error norms of the x and y axis weights rapidly decreased within hundreds of iterations and entered the stochastic steady-state bandwidth, fully demonstrating the effectiveness of the 0 < μ < 2 stable interval derived by the formula in actual operation. It is worth noting that although doubling the rotational speed leads to significant changes in the input frequency and sample distribution, the convergence curve shape remains consistent, reflecting the algorithm's good robustness to changes in operating conditions. Furthermore, the curve decreases faster at higher rotational speeds, indicating that NLMS's input energy normalization mechanism can improve sample utilization efficiency at higher frequencies.

[0113] After verifying the convergence of the overall weights, the estimation process of the amplitudes of each harmonic is further compared. Figure 5 The convergence trajectory of the amplitudes of the first five odd harmonics is shown. The solid line represents the real-time estimated value, and the dashed line represents the actual value. The results show that the algorithm can accurately identify multi-order harmonic components, providing a reliable basis for subsequent multi-frequency compensation.

[0114] To further evaluate the impact of the step size upper bound µmax on the convergence performance in the error-driven NLMS algorithm, Figure 6 The weight error norm was compared under three settings: µmax = 0.3, 0.6, and 1.0, at a speed of 6000 r / min. The convergence process was analyzed. Results showed that when µmax = 0.3, the curve was smoothest, the time to enter the steady-state error band was shortest, and it exhibited smaller steady-state mismatch when measurement noise was dominant. Increasing µmax could accelerate the update speed in the initial stage, but it introduced larger transient oscillations and increased the steady-state variance. Considering both convergence speed and steady-state accuracy, this paper selected µmax = 0.6 as the nominal parameter in subsequent experiments. In cases sensitive to noise and requiring high steady-state accuracy, µmax could be lowered to 0.3 to further reduce the mismatch.

[0115] This section has already derived the Lyapunov stability condition 0 < µ < 2. The experiment here verifies and quantifies the effect of µmax on the actual convergence speed and steady-state error.

[0116] Step 104, Harmonic component separation:

[0117] Let the target harmonic order be n=1,...,N DC components. The weighting coefficients ωx and ωy have the same dimensions as the displacement, and can be directly used for quantitative analysis and control gain setting.

[0118] The DC (bias) component can be obtained from the Adaline projection:

[0119]

[0120] The nth harmonic component is:

[0121]

[0122] The cosine / sine coefficients can be written in amplitude-phase form using standard polar coordinate transformation:

[0123]

[0124] Where Axn and Ayn represent the amplitudes of the nth harmonic. and This indicates its phase angle.

[0125] Therefore, it can be reconstructed as:

[0126]

[0127] Using the form atan(sin coefficient, cos coefficient) avoids quadrant ambiguity and maintains consistency with the order of coefficients in the formula.

[0128] The total harmonic displacement is obtained by superimposing the harmonics of each order:

[0129]

[0130] The separated DC and harmonic components provide a basis for the generation of subsequent compensation control force.

[0131] Figure 7 and Figure 8 A schematic diagram of the multi-harmonic NLMS displacement estimation structure is presented. The input basis vector R(k) consists of a DC term and cosine / sine components up to the Nth order, used to describe the fundamental and harmonic components of the rotor displacement signal. The corresponding weight vector... ,..., Driven by the estimation error εx(k), the normalized least mean square (NLMS) algorithm is used for adaptive updating to achieve real-time harmonic expansion and coefficient identification of the x-direction displacement. The y-channel adopts a completely consistent structure and update law. ,..., Online adjustments are made to achieve multi-harmonic estimation of displacement in the y-direction. Figure 7 and Figure 8The estimation block diagrams for the x-axis and y-axis directions are shown respectively. These two parts work together to provide accurate DC and multi-harmonic components for subsequent compensation control.

[0132] Step 2, design of the levitation force ELADRC;

[0133] Traditional PID controllers are widely used in bearingless motor suspension control due to their simple structure and convenient parameter tuning. However, they inherently rely on fixed-gain feedback regulation, lacking the ability to specifically observe and compensate for periodic disturbances and harmonic components caused by rotor eccentricity. Under high-speed or multi-frequency harmonic conditions, PID controllers often face a trade-off between response speed and steady-state accuracy, exhibiting limited convergence speed, sensitivity to parameter changes, and insufficient disturbance suppression. These shortcomings limit their application in strongly coupled systems such as CCR-BIM, necessitating the introduction of advanced control strategies capable of real-time observation and active compensation of total disturbances. To address this, this paper proposes a multi-frequency vibration suppression scheme based on Extended Linear Active Disturbance Rejection Control (ELADRC) to overcome the inherent defects of PID controllers and improve the robustness and disturbance rejection capability of the system.

[0134] Step 201, Traditional LADRC Design:

[0135] The derivation is based on the x-axis only; the process for the y-axis is similar. According to the formula, dividing both sides by m gives:

[0136]

[0137] make:

[0138]

[0139] The controlled object is then transformed into the standard double integral form of LADRC:

[0140]

[0141] As can be seen from the equation, the total disturbance fx explicitly includes the stiffness force and the external disturbance. The control input is characterized by the gain b and the control force u, which facilitates the introduction of LESO to estimate and compensate for fx in real time.

[0142] Define state:

[0143]

[0144] The system is written as follows:

[0145]

[0146] In the formula:

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] The corresponding LESO is:

[0155]

[0156] set up , , For the observed output. Expanding the formula, we get:

[0157]

[0158] make ,when hour,

[0159]

[0160] It is evident that the controlled object after compensation is equivalent to a double integral stage.

[0161] After compensating for the disturbance, a linear state error feedback (LSEF) control law is adopted, namely:

[0162]

[0163] in, As the displacement reference, u0 is the output control quantity of the Linear State Error Feedback (LSEF), and z1 and z2 are the LESO values ​​for displacement x and velocity x, respectively. The estimates are given by Kp2 and Kd2, which are the proportionality coefficient and differential coefficient, respectively. This forms the structure of LADRC as follows: Figure 9 As shown.

[0164] To evaluate the impact of key control parameters on the system's vibration reduction performance, this paper performs a sensitivity scan on a two-dimensional parameter plane containing the observer-controller bandwidth ratio ωo / ωc and the harmonic gain coefficient ke. Referring to typical engineering value ranges, ωo / ωc ∈ [3.7, 4.3] and ke ∈ [0.30, 0.40] are selected. The root mean square (RMS) value of the steady-state rotor displacement is calculated, and a three-dimensional surface is plotted, as shown below. Figure 10As shown in the figure. The results show that the RMS exhibits a distinct bimodal distribution with respect to ωo / ωc and ke. When the bandwidth ratio is close to 4.0 and the gain coefficient is approximately 0.35, the system vibration reaches its minimum and remains at a low level within a narrow range of ωo / ωc ∈ [3.7, 4.3] and ke ∈ [0.30, 0.40]. Beyond this range, the vibration reduction performance decreases significantly. This result verifies the crucial role of bandwidth matching between the observer and controller and the appropriate setting of harmonic mapping gain in comprehensive vibration suppression, providing a quantitative basis for engineering tuning. Based on the comprehensive analysis of the experimental data, subsequent experiments will use ωo / ωc = 4.0 and ke = 0.35 as nominal parameters and fine-tune them within the aforementioned narrow range to balance noise suppression and disturbance tracking requirements.

[0165] Further analysis reveals that the performance of LADRC is highly dependent on parameter tuning. The inertial time constant τ affects the system's overshoot suppression capability through trial and error; the control bandwidth ωc determines the response speed, but excessive bandwidth weakens noise immunity; the observer bandwidth ωo can improve disturbance tracking speed, but excessive bandwidth easily leads to noise sensitivity and oscillations; the control gain b is nominally determined by the mass m, but under conditions of parameter uncertainty and nonlinearity, it needs to be effectively compensated in conjunction with the observer. Especially in levitation force control, LADRC has an inherent contradiction: increasing ωc can speed up the response, but it forces ωo to increase synchronously, thus increasing noise sensitivity; if the observer bandwidth is too low, disturbance tracking will lag, and if it is too high, it will cause oscillations. Under complex operating conditions, these mutual constraints make parameter tuning particularly difficult. Thus, LADRC has a structural contradiction in the trade-off between "fast response and noise immunity," and its limitations urgently need to be overcome through structural improvements and algorithm extensions. Therefore, this paper proposes an improved LADRC design.

[0166] Step 202, Improved ELADRC Design:

[0167] Total disturbance extension modeling;

[0168] Considering harmonic vibrations, magnetic saturation, and unmodeled high-frequency terms, fx is extended to:

[0169]

[0170] In this equation, the first term of d(t) represents the multi-harmonic disturbance dynamically determined based on the rotational speed ωm; the second term, dsat(ψobs), represents the nonlinear disturbance induced by flux saturation; and the third term, dres, represents the unmodeled dynamics and high-frequency noise. This decomposition avoids redundant modeling with (1 / m)Fzx in the original equation and more clearly reveals the source of the disturbance.

[0171] LESO (Low-bandwidth scheduling)

[0172] To balance the estimation of low-frequency and high-frequency disturbances, observer bandwidth scheduling is introduced:

[0173]

[0174]

[0175] Wherein, ωo,base is used for tracking low-frequency non-harmonic disturbances; κNN(ωm)ωm reflects the bandwidth requirement of higher-order harmonic frequency growth; ωo,min and ωo,max are the amplitude limiting boundaries, respectively, to avoid lag due to excessively low values ​​or noise sensitivity due to excessively high values.

[0176]

[0177] In addition, to ensure separation of time scales, the following constraints must be met:

[0178]

[0179] This ensures that the observer responds faster than the controller, thus enabling rapid estimation and compensation of disturbances.

[0180] Adaptive gain for magnetic saturation;

[0181] To avoid overexcitation and distortion caused by flux saturation, a smoothing and limiting adaptive gain law is introduced:

[0182]

[0183] when As the saturation threshold ψmax approaches, the value of α automatically decreases, effectively reducing the control gain and enhancing the stability margin. The smoothing term εs is used to avoid the denominator being zero, ensuring numerical stability.

[0184] This constitutes the structure of ELADRC, as follows: Figure 11 As shown.

[0185] Step 3: Generation of harmonic compensation force;

[0186] Within the dual framework of Adaline harmonic decomposition and ELADRC, a dual-channel observation-compensation system is constructed: the rotor radial displacement x and y measured by the displacement sensor are processed by the Adaline module to extract the harmonic components of each order. , These harmonic information are incorporated into ELADRC to enhance the accuracy of total disturbance estimation, and directly fed into the compensator to generate harmonic compensation force. After being superimposed with the inner ring foundation levitation force command, the levitation winding is driven by force-current conversion to achieve multi-frequency vibration suppression.

[0187] Step 301, Calculation of compensating force:

[0188] Considering the superposition of low-frequency slowly varying disturbances and multiple harmonics, the ELADRC input disturbance is modeled as follows:

[0189]

[0190] Where fx,slow represents low-frequency, slowly varying disturbances. , This represents the nth harmonic component extracted by Adaline. ke is the mapping coefficient between harmonic displacement and equivalent disturbance; N is the highest harmonic order involved in the compensation.

[0191] For each harmonic, a corresponding compensation force is generated according to the principle of amplitude reverse compensation, and the gain is matched according to the amplitude:

[0192]

[0193] in, , These are the compensation gains for the nth harmonic in the x and y directions, respectively, which can be determined experimentally or by the principle of minimum variance.

[0194] Step 302, Magnetic saturation nonlinearity compensation:

[0195] Although the ELADRC inner loop already includes magnetic saturation adaptive gain, a smoothing and limiting nonlinear compensation module is further introduced to prevent excessive amplification of harmonic compensation force under extreme conditions. Its output is:

[0196]

[0197] Where Fmax is the single-axis compensation force limiting threshold, α(k) is the time-varying gain coefficient, and tanh() is the hyperbolic tangent function, used to smooth and limit the output amplitude and enhance the system stability margin.

[0198] To determine the input dimension of the Adaline / NLMS harmonic decomposer, this paper first performs power spectral density (PSD) analysis on the rotor displacement signal at two typical speeds of 3000 r / min and 6000 r / min, and calculates the integrated energy to evaluate the coverage capability for different harmonic orders N. The displacement energy coverage rate at different harmonic orders is compared as follows: Figure 12As shown, the results indicate that when only the fundamental frequency component N=1 is considered, the energy coverage of the x-axis displacement signal is approximately 86.2%, and the energy coverage of the y-axis displacement signal is 85.9%, which is clearly insufficient to describe the main vibration spectrum. When the order is expanded to N=3, the energy coverage of the x-axis displacement signal increases to approximately 94.8%, and the energy coverage of the y-axis displacement signal increases to approximately 94.1%. When the order is expanded to N=5, the coverage increases to 98.5% and 98.3%, respectively. When the order is expanded to N=7, the coverage increases to 99.1% and 98.9%, respectively. When the order is expanded to N=9, the coverage increases to 99.2% and 99.1%, respectively, with an improvement of less than 0.3%. Therefore, N=5 was selected as the harmonic order for both axes in the experiment. It can be seen that N=5 is sufficient to cover the main energy regions of the x-axis and y-axis vibration spectrum, and the input vector is updated in real time according to the formula when the rotational speed ωm changes beyond the threshold, ensuring the energy coverage and computational efficiency of harmonic decomposition under different operating conditions. The rotational speed ωm is monitored in real time, and the harmonic order N is updated when the speed change exceeds a threshold. The dynamic adjustment strategy avoids the computational burden caused by fixing high-order harmonics and also avoids the problem of insufficient high-frequency vibration compensation caused by fixing low-order harmonics, thus achieving an adaptive balance between accuracy and efficiency.

[0199] Step 303, Overall Control Force Synthesis:

[0200] The final control command is obtained by superimposing the ELADRC feedforward outputs Fx and Fy with the limited harmonic compensation force:

[0201]

[0202] Where Fx and Fy are the basic levitation force commands generated by the inner loop controller.

[0203] Step 4, Vibration Compensation Control Block Diagram;

[0204] Figure 13 A block diagram of the vibration compensation control system proposed in this paper is presented. The entire system adopts a dual closed-loop structure of rotational speed outer loop and levitation force inner loop to achieve real-time suppression of multi-frequency harmonic vibrations.

[0205] The outer loop controls the rotational speed: the mechanical angular velocity ωm is measured in real time by the rotational speed sampling module, and after PI regulation, an electromagnetic torque command is generated. This command is input to the air gap flux orientation controller to obtain the stator current reference value ( , Through dq / abc coordinate transformation and CRPWM inverter drive torque winding, closed-loop speed regulation is achieved.

[0206] The inner loop is for levitation force control: eddy current sensors collect rotor displacements x and y in real time as position feedback. On one hand, the displacement signal is directly input to the ELADRC levitation force controller, and the total disturbance is estimated by the Linear Extended State Observer (LESO). , The basic levitation force commands Fx and Fy are generated through linear state error feedback (LSEF). Simultaneously, the Adaline / NLMS Harmonic Decomposer is fed in, which constructs the input vector R(k) and updates the weight matrix Ω(k) online using the Normalized Least Mean Square (NLMS) algorithm, thereby extracting harmonic components of each order in real time. .

[0207] Harmonic components xh and yh are fed into a multi-harmonic compensator to calculate harmonic compensation forces Fxh and Fyh, and then smoothed by a nonlinear limiting module to obtain a limited output. , Subsequently, the harmonic compensation force after amplitude limiting and the basic levitation force generated by ELADRC are superimposed in the force / current transformation stage to form the total levitation force command. The instruction, through force-current conversion and inverse dq / abc transformation, yields a reference value for the levitation current. , Ultimately, the CRPWM drives the suspension winding to generate actual electromagnetic levitation force, thereby achieving synchronous suppression of fundamental frequency and multi-order harmonic vibrations.

[0208] Through this dual-closed-loop and dual-channel collaborative structure, the system can simultaneously ensure rotational speed stability and levitation force robustness under conditions of rotational speed variation and complex disturbances, achieving high-precision, multi-frequency band rotor vibration compensation.

[0209] The control parameters of the CCR-BIM system are shown in Table 1.

[0210] Table 1 Control Parameters

[0211]

[0212] Here is an example of an application of the present invention:

[0213] To verify the effectiveness and advancement of the proposed multi-frequency compensated Adaline–ELADRC control strategy, an experimental comparison scheme was designed and implemented. The experiment quantitatively compared the proposed method with three benchmark control strategies: traditional PID suspension force control, LADRC control, and Adaline–ELADRC control with only fundamental frequency compensation.

[0214] Simulation verification:

[0215] Figure 14 The rotor speed response under four control strategies was demonstrated. The reference speed was first accelerated from zero to 3000 r / min, and then further increased to 6000 r / min to verify the dynamic performance of different control strategies during the two speed change processes. All strategies achieved small overshoot and fast convergence speed in the first stage; however, in the second stage, due to the increased speed and enhanced disturbances, the settling time was relatively longer and the overshoot amplitude slightly increased, with PID and LADRC control exhibiting more pronounced fluctuations. The multi-frequency compensated Adaline-ELADRC control strategy, based on Adaline / NLMS harmonic decomposition, combined with bandwidth-scheduled ELADRC, multi-harmonic feedforward compensation, and nonlinear limiting, achieved comprehensive suppression of periodic disturbances. Compared with traditional PID, LADRC, and fundamental frequency-only compensation schemes, this method exhibited faster dynamic tracking capability during both speed change processes and achieved lower speed ripple in the steady-state ranges of 3000 r / min and 6000 r / min. The results show that the proposed multi-frequency compensation Adaline-ELADRC control strategy exhibits faster dynamic convergence speed and lower steady-state ripples in both stages of velocity change, thus verifying its effectiveness in multi-frequency vibration suppression and dynamic performance improvement.

[0216] Figure 15 Simulation results of x-axis vibration amplitude under four control strategies are presented. Simulation experiments were conducted at speeds of 3000 r / min and 6000 r / min, comparing the vibration suppression performance of traditional PID suspension control, LADRC control, Adaline-ELADRC control with only fundamental frequency compensation, and multi-frequency compensation Adaline-ELADRC control strategies. At 3000 r / min, the x-axis vibration amplitude of traditional PID suspension control was 22.3 µm, LADRC control was 15.1 µm, and Adaline-ELADRC control with only fundamental frequency compensation was 9.2 µm. The multi-frequency compensation Adaline-ELADRC control strategy further reduced the amplitude to 8.1 µm, representing reductions of 63.7%, 46.4%, and 12.0% compared to the other three methods, respectively. When the rotational speed increases to 6000 r / min, the corresponding vibration amplitudes are 56.1µm, 38.1µm, and 24.3µm, respectively, while the multi-frequency compensation Adaline-ELADRC control strategy only achieves 18.9µm, with reductions of 66.3%, 50.4%, and 22.2%, respectively.

[0217] Figure 16Simulation results of y-axis vibration amplitude under four control strategies are presented. Simulation experiments were conducted at speeds of 3000 r / min and 6000 r / min, comparing the vibration suppression performance of traditional PID suspension force control, LADRC control, Adaline-ELADRC control with only fundamental frequency compensation, and multi-frequency compensation Adaline-ELADRC control strategies. At 3000 r / min, the y-axis vibration amplitude of traditional PID suspension force control was 22.5 µm, LADRC control was 15.2 µm, and Adaline-ELADRC control with only fundamental frequency compensation was 9.3 µm. The multi-frequency compensation Adaline-ELADRC control strategy further reduced the amplitude to 8.2 µm, representing reductions of 63.6%, 46.1%, and 11.8% compared to the other three methods, respectively. When the rotational speed is increased to 6000 r / min, the corresponding vibration amplitude increases to 55.2 µm, 37.5 µm and 24.2 µm respectively, while the multi-frequency compensation strategy only reduces it to 19.1 µm, with reductions of 65.4%, 49.1% and 21.1% respectively.

[0218] like Figure 17-20 As shown, the rotor shaft end trajectories of four control strategies at speeds of 3000 r / min and 6000 r / min are compared. Quantitative analysis shows that the maximum trajectory diameters corresponding to each control strategy are: PID control 31.6 µm / 76.1 µm, LADRC control 21.4 µm / 51.2 µm, Adaline / NLMS–ELADRC control with only fundamental frequency compensation 13.2 µm / 30.3 µm, and the multi-frequency harmonic vibration compensation control proposed in this paper 11.6 µm / 27.6 µm. Performance evaluation based on the multi-frequency compensation strategy shows that at 3000 r / min, its trajectory diameter is reduced by 63.3%, 45.8%, and 12.1% compared to the PID, LADRC, and fundamental frequency compensation strategies, respectively; at 6000 r / min, the corresponding reductions are 63.7%, 46.1%, and 8.9%, respectively, indicating that the proposed method can significantly suppress the rotor trajectory amplitude at different speeds.

[0219] Simulation results combining x-axis, y-axis, and shaft end trajectory demonstrate that the multi-frequency compensated Adaline–ELADRC control strategy significantly outperforms traditional PID suspension control, LADRC control, and Adaline–ELADRC control with only fundamental frequency compensation under both 3000 r / min and 6000 r / min operating conditions. The proposed compensation strategy achieves greater reduction in vibration amplitude across both axes and the overall rotor trajectory, exhibiting excellent multi-frequency disturbance suppression capability and strong robustness, validating its comprehensive advantages under both low-speed and high-speed operating conditions.

[0220] Experimental verification:

[0221] To verify the effectiveness and robustness of the proposed multi-frequency compensated Adaline–ELADRC control strategy in a real-world system, an experimental platform for a bearingless composite rotor squirrel-cage induction motor (CCR-BIM) was built. The control core utilizes a TMS320F28335 digital signal processor (DSP), synchronously executing torque vector control and levitation force control at a 10 kHz interrupt frequency. Both control tasks are completed within the same interrupt cycle to ensure real-time coordination and determinism. The hardware architecture of the experimental platform is as follows: Figure 21 As shown: the upper layer is the torque winding power drive board, the lower layer is the suspension winding power drive board, and the middle layer is the DSP control board. The currents of both windings are acquired by Hall current sensors, conditioned by the interface circuit, and then sent to the DSP's analog-to-digital converter (ADC) channel; the rotor radial position signal is measured in real time by an eddy current sensor and sent to the ADC for synchronous sampling via the same conditioning link. The main parameters of CCR-BIM are shown in Table 2.

[0222] Table 2 CCR-BIM Motor Parameters

[0223]

[0224] Figure 22 The speed response curves for four control methods are presented, corresponding to traditional PID suspension control, LADRC control, Adaline-ELADRC control with only fundamental frequency compensation, and multi-frequency compensated Adaline-ELADRC control strategy. In the experiment, the motor was started from standstill, first accelerated and stabilized at 3000 r / min, and then further increased to 6000 r / min to compare the impact of different control strategies on rotor vibration suppression performance.

[0225] like Figure 23 As shown, under the condition of 3000 r / min, the steady-state vibration amplitudes along the x-axis for the four control methods are, in descending order: traditional PID suspension force control 34.8 µm, LADRC control 23.3 µm, Adaline–ELADRC control with only fundamental frequency compensation 18.8 µm, and the multi-frequency compensation Adaline–ELADRC control strategy 12.4 µm. Compared with the first three methods, the multi-frequency compensation strategy achieves reductions of 64.4%, 46.8%, and 34.0%, respectively. When the speed increases to 6000 r / min, the corresponding vibration amplitudes increase to 121.1 µm, 87.3 µm, 73.3 µm, and 51.1 µm, respectively. The multi-frequency compensation strategy still achieves reductions of 57.8%, 41.5%, and 30.3% compared to the above three methods.

[0226] like Figure 24As shown, under the condition of 3000 r / min, the vibration amplitude of the y-axis displacement is as follows: 43.2 µm for traditional PID suspension force control, 23.7 µm for LADRC control, 19.8 µm for Adaline–ELADRC control with only fundamental frequency compensation, and 12.5 µm for the multi-frequency compensation Adaline–ELADRC control strategy. Compared with the first three methods, the vibration amplitude of the multi-frequency compensation strategy is reduced by 71.1%, 47.3%, and 36.9%, respectively. When the speed is increased to 6000 r / min, the corresponding vibration amplitude increases to 144.2 µm, 89.6 µm, 74.4 µm, and 49.5 µm. The multi-frequency compensation strategy still achieves a reduction of 65.7%, 44.8%, and 33.5% compared with the first three methods.

[0227] like Figure 25 As shown, under the condition of 3000 r / min, the maximum amplitude of the rotor trajectory for the four control methods are: traditional PID 42.1 µm, LADRC 25.2 µm, Adaline-ELADRC with only fundamental frequency compensation 20.6 µm, and the proposed multi-frequency compensation Adaline-ELADRC 16.2 µm. Compared with the first three, the amplitude reduction of the proposed method is 61.6%, 35.7%, and 21.4%, respectively. When the speed increases to 6000 r / min, the corresponding values ​​are 98.2 µm, 76.3 µm, 64.2 µm, and 46.8 µm, respectively, and the reduction of the proposed method is 52.4%, 38.7%, and 27.1%, respectively. The results show that the proposed multi-frequency compensation Adaline-ELADRC can significantly reduce the rotor trajectory amplitude at different speeds, and its vibration suppression performance is better than the comparative methods.

[0228] Experimental results combining x-axis, y-axis, and rotor trajectory measurements show that the multi-frequency compensated Adaline–ELADRC control strategy significantly outperforms traditional PID suspension control, LADRC control, and Adaline–ELADRC control with only fundamental frequency compensation at both 3000 r / min and 6000 r / min speeds. These results demonstrate that as the rotational speed changes from low to high, the multi-frequency compensated Adaline–ELADRC control strategy achieves greater vibration suppression in both axial directions and the overall trajectory, exhibiting superior multi-frequency disturbance suppression capability and strong robustness.

[0229] It is understood that data preprocessing methods known to those skilled in the art include data cleaning, data transformation, and data reduction. Data transformation includes type conversion and normalization and standardization. Although the dimensions and types of data were omitted in the description of the preceding embodiments, data preprocessing is a technical knowledge known to those skilled in the art and a prerequisite step in data processing. Therefore, the previously described well-known data preprocessing steps were not described independently.

[0230] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A bearingless compound rotor cage asynchronous motor multi-frequency harmonic vibration compensation control method, characterized in that, The method comprises the following steps: Real-time acquisition of rotor radial displacement signals of a bearingless compound rotor cage asynchronous motor; The input vector containing direct current term and multi-order cosine and sine components is constructed, the displacement signal is decomposed in real time by adaptive linear neuron algorithm, the direct current component, fundamental wave component and each order harmonic component are extracted, the displacement signal is decomposed in real time by adaptive linear neuron algorithm specifically includes: constructing input vector, the input vector contains direct current term 1 and cosine and sine components from base frequency to Nth order; the weight matrix of x axis and y axis is initialized; the estimated displacement is calculated by linear combination of weight matrix and input vector; the error between actual displacement and estimated displacement is calculated; the weight matrix is updated by using normalized least square algorithm, the update law is that the increment of weight is equal to the ratio of adaptive step and energy normalization factor of input vector multiplied by the product of error and input vector; the amplitude and phase information of each order harmonic is extracted from the updated weight matrix, wherein the x axis nth order harmonic amplitude is , the phase is , the y axis nth order harmonic amplitude is , and the phase is ; An extended linear active disturbance rejection controller is used to observe total disturbance of the system, which includes low-frequency slow-changing disturbance and harmonic disturbance; Corresponding harmonic compensation forces are calculated according to the extracted harmonic components; The harmonic compensation forces are superimposed with the basic suspension force output by the extended linear active disturbance rejection controller to generate total control force instructions; After force-current conversion, the total control force instructions drive the suspension winding to realize suppression of rotor multi-frequency harmonic vibration.

2. Bearingless composite-rotor cage-type asynchronous motor multi-frequency harmonic vibration compensation control method according to claim 1, characterized in that, The adaptive step size is dynamically adjusted according to the estimation error, specifically: The adaptive step size is equal to the ratio of the maximum step size to the absolute value of the error multiplied by the inverse of the sum of the absolute value of the error and the smoothing factor; The maximum step size is in the range of 0 to 2 to ensure the convergence of the algorithm.

3. Bearingless composite-rotor cage-type asynchronous motor multi-frequency harmonic vibration compensation control method according to claim 1, characterized in that, The extended linear active disturbance rejection controller comprises: A linear extended state observer is used to estimate three state variables of displacement, speed and total disturbance; A bandwidth scheduling mechanism is used to dynamically adjust the observer bandwidth according to the speed and the highest harmonic order; A magnetic saturation adaptive gain module is used to adjust the control gain according to the flux linkage observation value; A linear state error feedback control law is used to generate control output based on displacement error and speed estimation.

4. The bearingless compound rotor cage-type asynchronous machine multi-frequency harmonic vibration compensation control method according to claim 3, characterized in that, The bandwidth scheduling mechanism is specifically: The observer bandwidth takes the larger value between the basic bandwidth and the speed-related bandwidth, and is limited between the preset minimum value and maximum value; The speed-related bandwidth is equal to the product of the bandwidth coefficient and the highest harmonic order and the rotor angular velocity; The observer bandwidth is always maintained at 3 to 5 times the controller bandwidth to ensure time scale separation.

5. The bearingless composite-rotor cage-type asynchronous machine multi-frequency harmonic vibration compensation control method according to claim 3, characterized in that, The gain adjustment strategy of the magnetic saturation adaptive gain module is: The adaptive gain is equal to the product of the basic gain and the hyperbolic tangent function; The argument of the hyperbolic tangent function is the ratio of the flux linkage saturation threshold to the sum of the observed flux linkage amplitude and the smoothing term; When the observed flux linkage approaches the saturation threshold, the adaptive gain is automatically reduced.

6. The bearingless composite-rotor cage-type asynchronous machine multi-frequency harmonic vibration compensation control method according to claim 1, characterized in that, The calculation of the corresponding harmonic compensation force according to the extracted harmonic components specifically includes: The extracted harmonic components are multiplied by the corresponding compensation gain coefficients; All harmonic compensation force components are summed up; The compensation force is smoothed and limited by a nonlinear amplitude limiting function to prevent overcompensation.

7. The bearingless composite-rotor cage-type asynchronous machine multi-frequency harmonic vibration compensation control method according to claim 6, characterized in that, The nonlinear amplitude limiting function is: The amplitude-limited compensation force is equal to the product of the time-varying gain coefficient, the maximum compensation force limit, and the hyperbolic tangent function; The argument of the hyperbolic tangent function is the ratio of the compensation force to the maximum compensation force limit.

8. Bearingless composite-rotor cage-type asynchronous machine multi-frequency harmonic vibration compensation control method according to any of claims 1 to 7, characterized in that, Further comprising: Determining the highest harmonic order N that needs to be compensated according to power spectral density analysis; When the speed change exceeds the preset threshold, dynamically updating the frequency components in the input vector; The control method is executed in a digital signal processor at a fixed sampling frequency.

9. A bearingless compound rotor cage asynchronous motor multi-frequency harmonic vibration compensation control system for executing the bearingless compound rotor cage asynchronous motor multi-frequency harmonic vibration compensation control method according to any one of claims 1 to 8, characterized in that, It comprises: A displacement sensor module is used to real-time acquisition of rotor radial displacement in x and y directions; An adaptive harmonic decomposition module is used to implement an adaptive linear neuron algorithm to decompose the displacement signal and extract harmonic components; An extended active disturbance rejection control module is used to observe the total disturbance of the system and generate basic suspension force instructions; A harmonic compensation force calculation module is used to generate compensation forces according to harmonic components; a force synthesis module for superimposing the basic levitation force and the harmonic compensation force; a force-to-current conversion module for converting the force command into a current command; a power drive module for driving the levitation windings to generate the electromagnetic levitation force.

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